Engineered Solutions: The Case for 3D Geotechnical Analysis
By Dr. Murray Fredlund, strategic advisor, Geotechnical, Bentley Systems
There are ongoing discussions in the geotechnical community about the need to perform 3D analysis. The questions raised relate to the results achieved when performing a 3D analysis vs. the results of a traditional 2D analysis. While the industry has largely embraced the 2D approach as an accepted method of practice, important questions still need to be answered, including the following:
- Is there a difference when calculating the Factor of Safety (FOS) in 3D vs. 2D?
- What are the advantages of a 3D analysis?
- What are the practical differences when using 3D slope stability analysis?
- What cases favor the use of 3D analysis?
The True Factor of Safety
There’s a fundamental difference between calculations of FOS for failed slopes using 2D as opposed to 3D analysis. While geotechnical engineers have become complacent with the use of 2D slope stability analysis (easy to perform), 2D methods suffer from the following fundamental limitations: the slip shape is assumed to be cylindrical; the slope geometry, geo-strata and water table are assumed to be unchanged in the third dimension; and shear on the end surfaces is not considered.
The differences between 2D and 3D analysis and FOS calculations are closely related to the geometry of the model and the critical slip surface. It’s known that a 3D FOS will almost always be higher, and research has put the level of difference between 15 and 50 percent. The exact level of difference must be computed for each individual scenario. Therefore, it’s recommended to run both 2D and 3D analysis to identify the exact difference between the two FOS calculations. Professional judgment can then be applied to interpret the model results.
In general, geotechnical engineers should pay close attention to the following six factors, which could affect FOS calculations:
- The slip surface shape
- Water table
- Distributed/point loads
3D Analysis Is a More Rigorous Representation of the Real World
After 20-plus years of research, it’s undisputed in academic circles that 3D analysis is a more rigorous representation of reality. And the closer the computed FOS for a slope to the reality, the more accurate the analysis.
Consider the following scenarios:
Levee analysis: For levees, the earth used for construction is quite costly, and levees can extend over many miles. When using 2D analysis, an over-design of the levee structures might result in increased costs to construct. There’s the potential to model levee intersections to improve design.
Deep foundations: When designing high-rise buildings, minimizing the foundation settlements is required to limit the damage of the superstructures. Three-dimensional analysis provides a more realistic assessment of stresses and displacements as well as structural forces from cylindrical and square-volume piles.
Tailings facilities: Recent failures of tailing dams have focused more attention on stability analysis. Three-dimensional stability analysis of complex tailings structures allows for a more accurate understanding of the long-term performance of such structures.
Heap leach analysis: Larger amounts of ore can be extracted on a heap leach pile with steep side slopes. However, the increased steepness of the side slope results in a condition closer to failure. In this case, 3D analysis can more closely represent the geometry of the heap leach pile. It’s important to accurately balance the slope-angle design and the ore recovery.
The Special Case of Back Analysis
Another important 3D application with significant ramifications is the case of back-analysis of a failure. Typically, geotechnical engineers are doing back-analysis in 2D, resulting in a FOS 1.0, which overestimates the strength of the materials in the slope. Using 3D will yield material property strengths that are lower than 2D back-analysis but are more realistic.
As a result, if you do a back-analysis using 2D and then attempt a forward analysis with 3D, you will overestimate the FOS on the slope, which causes a perilous condition. The engineer should always use 3D for back analysis to accurately determine the material strengths.
More than 20 years of research clearly show that 3D analysis is the better and more rigorous tool for slope stability analysis. And while the primary reason for the greater popularity of 2D was its simplicity, now there are advanced software technologies to allow for simultaneous, easy and fast 3D analysis with sound computation methods. And the improved 3D FOS calculations can affect professional design and project-related costs.